Hello clarinet and welcome to JustAnswer.
Traffic courts deal with this kind of situation all of the time and it generally is not a big deal if you take care of it quickly.
The best thing to do would be to take copies of your paperwork to the court where you were supposed to appear, go to the traffic clerk's window and explain what happened. You should be able to clear it up right there in the clerk's office, particularly if the check was received, even though it went to the wrong place.
At worst, you may have to reset the court date for an appearance to explain what happened to the court, but that is very unlikely based on what you've said here.
Don't let this go for too long, though, as the court will eventually issue an arrest warrant
for the failure to appear. Once that happens, a court appearance will be necessary for sure and you run the risk of getting arrested if stopped for some other traffic violation.
Thanks for asking your question here on JustAnswer and good luck getting this squared away. If you have any other questions, please let me know.